The quantification of micro-vasculatures is important for the analysis of angiogenesis on which the detection of tumor growth or hepatic fibrosis depends. Synchrotron-based X-ray computed micro-tomography (SR-mCT) allows rapid acquisition of micro-vasculature images at micrometer-scale spatial resolution. Through skeletonization, the statistical features of the micro-vasculature can be extracted from the skeleton of the micro-vasculatures. Thinning is a widely used algorithm to produce the vascular skeleton in medical research. Existing three-dimensional thinning methods normally emphasize the preservation of topological structure rather than geometrical features in generating the skeleton of a volumetric object. This results in three problems and limits the accuracy of the quantitative results related to the geometrical structure of the vasculature. The problems include the excessively shortened length of elongated objects, eliminated branches of blood vessel tree structure, and numerous noisy spurious branches. The inaccuracy of the skeleton directly introduces errors in the quantitative analysis, especially on the parameters concerning the vascular length and the counts of vessel segments and branching points. In this paper, a robust method using a consolidated end-point constraint for thinning, which generates geometry-preserving skeletons in addition to maintaining the topology of the vasculature, is presented. The improved skeleton can be used to produce more accurate quantitative results. Experimental results from high-resolution SR-mCT images show that the end-point constraint produced by the proposed method can significantly improve the accuracy of the skeleton obtained using the existing ITK three-dimensional thinning filter. The produced skeleton has laid the groundwork for accurate quantification of the angiogenesis. This is critical for the early detection of tumors and assessing anti-angiogenesis treatments.